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Mathematical Treasure: De Morgan’s Elements of Algebra

Author(s):

Frank J. Swetz (The Pennsylvania State University)

Augustus De Morgan (1806-1871) was a British mathematician, perhaps best remembered today for his work in logic. In De Morgan’sElements of Algebra (1835), a reader begins to realize the conceptual problems of algebra. Just what is algebra? Is it merely arithmetic using symbols rather than numbers? These were controversial questions at the time.

On pages 44 and 45, the issue of “negative numbers” is confronted: Do they exist? If so, how does one work with them?

On page 151 of his Algebra, De Morgan considered the hazards of treating “0” as an independent quantity within operations.

The images above are presented courtesy of the University of Pennsylvania Libraries.